Question
-> I get this error: 'Error: Server Verification Failed.' when I connect to some servers
Answer
This error typically means that the Game Server you are trying to connect to is unable to contact the Steam Authentication Servers.
You should try several servers to see if just one is having problems or all are.
This could be due to an internet problem or a problem with the Authentication Servers.
You can always look at the Steam Status Page and see if there is something going on:
http://www.steampowered.com/status/status.html
Be sure to look at the time on the graph, if it hasn't updated in a while then that is a sure sign that things are getting hung up.
If you still getting this error even if things look normal and there are no other reports of problems on the Steam Forums, please log out of Steam then start Steam back up and try connecting again.
If there has been a recent Steam update, some Servers may need to be restarted before they clear the error on their end, so be sure to try a few different Servers if you see this problem.
Router Firmware
If this has been a persistant problem then there is a good chance that you have a bad firmware version in your router. Some firmware versions from Linksys can cause this problem.
You can verify this by connecting to a spectator server or any insecure server. If you can connect and spectate or play on insecure servers but not on secure servers then almost certainly this is your problem.
If you ever get any disconnects from servers with messages about hot errors or parse errors then this also applies.